De Maesschalck Canard Cycles 9783030792350

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Автор: De Maesschalck
Название: Canard Cycles
ISBN: 9783030792350
Издательство: Springer
Классификация:

Кибернетика и теория систем

Основы высшей математики и математический анализ

Теории нелинейных процессов

Динамика и вибрация

ISBN-10: 3030792358
Обложка/Формат: Soft cover
Страницы: 408
Вес: 0.66 кг.
Дата издания: 23.08.2022
Серия: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Язык: English
Издание: 1st ed. 2021
Иллюстрации: 42 illustrations, color; 59 illustrations, black and white; xxi, 408 p. 101 illus., 42 illus. in color.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: From Birth to Transition
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs. In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure. The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilberts 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh–Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points.
Дополнительное описание: Part I Basic Notions.- 1 Basic Definitions and Notions.- 2 Local Invariants and Normal Forms.- 3 The Slow Vector Field.- 4 Slow-Fast Cycles.- 5 The Slow Divergence Integral.- 6 Breaking Mechanisms.- 7 Overview of Known Results.- Part II Technical Tools.-

Canard Cycles, De Maesschalck